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from sympy.core.expr import ExprBuilder
from sympy.core.function import (Function, FunctionClass, Lambda)
from sympy.core.symbol import Dummy
from sympy.core.sympify import sympify, _sympify
from sympy.matrices.expressions import MatrixExpr
from sympy.matrices.matrixbase import MatrixBase
class ElementwiseApplyFunction(MatrixExpr):
r"""
Apply function to a matrix elementwise without evaluating.
Examples
========
It can be created by calling ``.applyfunc(<function>)`` on a matrix
expression:
>>> from sympy import MatrixSymbol
>>> from sympy.matrices.expressions.applyfunc import ElementwiseApplyFunction
>>> from sympy import exp
>>> X = MatrixSymbol("X", 3, 3)
>>> X.applyfunc(exp)
Lambda(_d, exp(_d)).(X)
Otherwise using the class constructor:
>>> from sympy import eye
>>> expr = ElementwiseApplyFunction(exp, eye(3))
>>> expr
Lambda(_d, exp(_d)).(Matrix([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]]))
>>> expr.doit()
Matrix([
[E, 1, 1],
[1, E, 1],
[1, 1, E]])
Notice the difference with the real mathematical functions:
>>> exp(eye(3))
Matrix([
[E, 0, 0],
[0, E, 0],
[0, 0, E]])
"""
def __new__(cls, function, expr):
expr = _sympify(expr)
if not expr.is_Matrix:
raise ValueError("{} must be a matrix instance.".format(expr))
if expr.shape == (1, 1):
# Check if the function returns a matrix, in that case, just apply
# the function instead of creating an ElementwiseApplyFunc object:
ret = function(expr)
if isinstance(ret, MatrixExpr):
return ret
if not isinstance(function, (FunctionClass, Lambda)):
d = Dummy('d')
function = Lambda(d, function(d))
function = sympify(function)
if not isinstance(function, (FunctionClass, Lambda)):
raise ValueError(
"{} should be compatible with SymPy function classes."
.format(function))
if 1 not in function.nargs:
raise ValueError(
'{} should be able to accept 1 arguments.'.format(function))
if not isinstance(function, Lambda):
d = Dummy('d')
function = Lambda(d, function(d))
obj = MatrixExpr.__new__(cls, function, expr)
return obj
@property
def function(self):
return self.args[0]
@property
def expr(self):
return self.args[1]
@property
def shape(self):
return self.expr.shape
def doit(self, **hints):
deep = hints.get("deep", True)
expr = self.expr
if deep:
expr = expr.doit(**hints)
function = self.function
if isinstance(function, Lambda) and function.is_identity:
# This is a Lambda containing the identity function.
return expr
if isinstance(expr, MatrixBase):
return expr.applyfunc(self.function)
elif isinstance(expr, ElementwiseApplyFunction):
return ElementwiseApplyFunction(
lambda x: self.function(expr.function(x)),
expr.expr
).doit(**hints)
else:
return self
def _entry(self, i, j, **kwargs):
return self.function(self.expr._entry(i, j, **kwargs))
def _get_function_fdiff(self):
d = Dummy("d")
function = self.function(d)
fdiff = function.diff(d)
if isinstance(fdiff, Function):
fdiff = type(fdiff)
else:
fdiff = Lambda(d, fdiff)
return fdiff
def _eval_derivative(self, x):
from sympy.matrices.expressions.hadamard import hadamard_product
dexpr = self.expr.diff(x)
fdiff = self._get_function_fdiff()
return hadamard_product(
dexpr,
ElementwiseApplyFunction(fdiff, self.expr)
)
def _eval_derivative_matrix_lines(self, x):
from sympy.matrices.expressions.special import Identity
from sympy.tensor.array.expressions.array_expressions import ArrayContraction
from sympy.tensor.array.expressions.array_expressions import ArrayDiagonal
from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
fdiff = self._get_function_fdiff()
lr = self.expr._eval_derivative_matrix_lines(x)
ewdiff = ElementwiseApplyFunction(fdiff, self.expr)
if 1 in x.shape:
# Vector:
iscolumn = self.shape[1] == 1
for i in lr:
if iscolumn:
ptr1 = i.first_pointer
ptr2 = Identity(self.shape[1])
else:
ptr1 = Identity(self.shape[0])
ptr2 = i.second_pointer
subexpr = ExprBuilder(
ArrayDiagonal,
[
ExprBuilder(
ArrayTensorProduct,
[
ewdiff,
ptr1,
ptr2,
]
),
(0, 2) if iscolumn else (1, 4)
],
validator=ArrayDiagonal._validate
)
i._lines = [subexpr]
i._first_pointer_parent = subexpr.args[0].args
i._first_pointer_index = 1
i._second_pointer_parent = subexpr.args[0].args
i._second_pointer_index = 2
else:
# Matrix case:
for i in lr:
ptr1 = i.first_pointer
ptr2 = i.second_pointer
newptr1 = Identity(ptr1.shape[1])
newptr2 = Identity(ptr2.shape[1])
subexpr = ExprBuilder(
ArrayContraction,
[
ExprBuilder(
ArrayTensorProduct,
[ptr1, newptr1, ewdiff, ptr2, newptr2]
),
(1, 2, 4),
(5, 7, 8),
],
validator=ArrayContraction._validate
)
i._first_pointer_parent = subexpr.args[0].args
i._first_pointer_index = 1
i._second_pointer_parent = subexpr.args[0].args
i._second_pointer_index = 4
i._lines = [subexpr]
return lr
def _eval_transpose(self):
from sympy.matrices.expressions.transpose import Transpose
return self.func(self.function, Transpose(self.expr).doit())
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